NUS CS5247

Using a PRM Planner to Using a PRM Planner to Compare Centralized Compare Centralized

and Decoupled and Decoupled Planning for Multi-Planning for Multi-

Robot SystemsRobot SystemsBy Gildardo Sánchez and Jean-Claude By Gildardo Sánchez and Jean-Claude

LatombeLatombeIn Proc. IEEE Int. Conf. on In Proc. IEEE Int. Conf. on

Robotics and Automation 2002 Robotics and Automation 2002

Presented by Melvin ZhangPresented by Melvin Zhang

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Overview Motivation Coordinating multiple robots Centralized planning Decoupled planning SBL planner Experiment setup Results Summary Comments

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Motivation Some industrial settings (spot welding) requires

4-10 robots with 20-60 dof each Manual programming

time consuming and error prone Multi robot planning can be classified as

centralized decoupled

Decoupled approach is prevalent, as lost of completeness is assumed to be small

How valid is this statement?

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Coordinating multiple robots (Demo)

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Coordinating multiple robots Assuming p robots with n dof each Centralized planning

Treat multiple robots as a single robot Plan in the composite C-space Complexity ~ enp

Decoupled planning Plan for each robot independently Coordinate them later Complexity ~ pen

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Centralized planning Reduce problem to planning for single robot Collisions between robots are self-collisions of

the single composite robot Advantages

Complete, if the underlying planner is complete Drawbacks

Computationally expensive, Not applicable when global state of all robots is

unknown

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Decoupled planning Plans path of each robot independently Coordinate them later Several schemes

Velocity turning Robot prioritization

Advantages Faster as C-space has fewer dimensions

Drawbacks Incomplete No coordinated trajectory of paths found in first phase

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Decoupled planning – Two schemes Velocity tuning

Separately plan a path of each robot to avoid collision with obstacles

Compute the trajectory of the robots to avoid inter-robot collision

Global coordination – plan in [0,1]p

Pairwise coordination – plan in [0,1]2

After path is fixed, dof of each robot is 1

Pairwise coordination plan s1 and s2

plan s1,2 with s3, ... plan s1,...,n-1 with sn

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Decoupled planning – Two schemes Robot prioritization

Plan path of the first robot in its C-space Plan trajectory of ith robot assuming that robots

1,…,i-1 are moving obstacles

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Decoupled planning - Incompleteness Initial configuration Goal configuration

Paths generated in first phase No coordinated solution found in second phase

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SBL planner Single-query

Roadmap is used to answer a single planning query Bi-directional

Grow a tree of milestones from both start and end configuration

Lazy in checking collision Avoid unnecessary collision checking on edges 4-40 times faster than classical single-query

bidirectional PRM planner

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Characteristics of SBL planner

Plot of number of failure vs max milestones allowed (S) Two thresholds Smin and Smax for a problem instance If (S < Smin) planner fails consistently If (S > Smax) planner succeeds consistently

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Experiment setup Planners

Centralized planning (C-SBL) Decoupled planning, global coordination (DG-SBL) Decoupled planning, pairwise coordination (DP-SBL)

Three problem instances, {PI, PII, PIII} Number of robots involved, {2, 4, 6} Number of runs

100 for C-SBL 20 for DG-SBL and DP-SBL

For each call to the SBL planner, at most 50,000 milestones are allowed

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Problem I

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Problem II

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Problem III

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Results – C-SBL Result for C-SBL

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Results – Failure rate

Rate of failure increases sharply for 4 and 6 robots Failure occurs during coordination Successful run of decoupled planner, no of milestones smaller than

50,000 -> failure due to incompleteness of decoupled approach

Comparison of failure rate

0

10

20

30

40

50

60

70

80

90

PI-2 PI-4 PI-6 PII-2 PII-4 PII-6 PIII-2 PIII-4 PIII-6

Problem instance

Perc

enta

ge o

f fai

lure

s

DG-SBL

DP-SBL

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Results – Running time

Running time for all 3 planners are comparable Centralize planning is feasible using SBL planner

Comparison of running time

0

50

100

150

200

250

300

350

400

450

500

PI-2 PI-4 PI-6 PII-2 PII-4 PII-6 PIII-2 PIII-4 PIII-6

Problem instance

Run

ning

tim

e

C-SBL

DG-SBL

DP-SBL

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Summary Decoupled planning may not find a solution

when tight coordination is required Loss of completeness is significant in practice

Using SBL, planning time for decoupled and centralized planning is comparable Centralized planning is technically feasible

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Comments Tight coordination is specified using specific

problem instances Similar to the concept of expansiveness, is it possible

to develop some characterization of “tight coordination”?

Centralized and decoupled can be viewed as two extremes of coordination Can we find a continuum of planners in which the

level of coordination can be parameterized? One idea is to use a hierarchy of robots

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Thank you for listening Questions ?

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